Dynamic rendering of ink strokes with transparency

ABSTRACT

Apparatus and methods for dynamically rendering transparent ink strokes, in some situations such that the rendered ink stroke has transparency similar to physical ink while it is being drawn. For example, the ink stroke may be dynamically rendered as a stroke having uniform transparency while it is being drawn. Only the new ink segment that has most recently been added to the stroke may be drawn, and areas of the new ink segment that overlap older segments of the ink stroke may be frozen, or excluded from being repainted.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.09/918,484, filed Aug. 1, 2002 and titled “Dynamic Rendering of InkStrokes with Transparency,” now U.S. Pat. No. 6.707,473 This applicationis related to U.S. patent application Ser. No. 09/918,721, entitled“Rendering Ink Strokes of Variable Width and Angle,” filed Aug. 1, 2001,and U.S. patent application Ser. No. 09/852,799, entitled “SerialStorage of Ink and its Properties,” filed May 11, 2001. All of saidapplications are hereby incorporated by reference as to theirentireties.

FIELD OF THE INVENTION

The present invention is directed generally to rendering transparentdigital ink, and more particularly to improved ways of renderingtransparent digital ink dynamically.

BACKGROUND OF THE INVENTION

The term “digital ink” refers to one or more strokes that are recordedfrom a pointing device, such as a mouse, a stylus/pen on a digitizertablet, or a stylus/pen on a display screen integrated with a digitizertablet (e.g., a touch-sensitive display screen). As used herein, theterm “ink” is shorthand for digital ink. Also, the term “pen” and“stylus” are used generically and interchangeably. Each stroke may bestored as one or more ink packets, in which each ink packet may containcoordinates (x, y) corresponding to the position of the pointing device.For example, a user may move a pen along a touch-sensitive displayscreen of a computer system so as to draw a line or curve, and thecomputer system may sample the coordinates (x, y) along the trajectoryof the pen tip position over time (or on any other interval as known inthe art) as the user moves the pen. These coordinates represent pointsalong the curve or line and are stored as ink packets.

Ink may be either transparent or non-transparent, as used herein. Inkthat is transparent means that the ink does not fully conceal thebackground behind it when displayed on a display or printed on aprinter. Ink that is not transparent completely conceals or occludes thebackground behind it. Non-transparent ink may also be referred to asopaque ink. For instance, FIG. 1 shows ink strokes 101, 102, and 103.Ink strokes 102 and 103 each overlay ink stroke 101, but ink stroke 103completely conceals its background, including the portion of ink stroke101 that it overlays (i.e., the portion of ink stroke 101 that is abackground behind ink stroke 103). Thus, ink stroke 103 is consideredopaque. In contrast, ink stroke 102 allows some of ink stroke 101, aswell as some of the white background, to show through where ink stroke102 overlays ink stroke 101. Thus, ink stroke 102 is consideredtransparent. Ink can be of any transparency and still be consideredtransparent. Current graphics interfaces are capable of applyingtransparent paint with a prescribed degree of transparency. For example,ink may be 50% transparent, which means that 50% of the background isconcealed, or ink may be 25% transparent, which means that 75% of thebackground is concealed. A transparent ink stroke can be analogized witha piece of glass, such as colored glass, in which objects behind theglass can be seen. A non-transparent ink stroke can be analogized with abrick wall that hides everything behind it.

It is often desirable to render a transparent ink stroke dynamicallywhile the ink stroke is being drawn, in other words, to draw the inkstroke on the display screen while the pointing device moves and addsnew points to the ink stroke or strokes. One way to accomplish this isto erase the entire screen and redraw everything on the screen each timea new point is added to the ink stroke. This is an imperfect solution,however, since in practice there is typically a short time intervalbetween ink points, and repeatedly clearing and redrawing the screenuses massive amounts of processing power, not to mention causing thescreen to flicker. A way to reduce the redrawing time would be draw eachnew segment of an ink stroke as it is drawn. The problem with this isthat the transparencies of the overlapping portion of ink segments arereduced in an unexpected and unintended manner. The effect of redrawingtransparent ink is shown in FIG. 2, where the darker circles of an inkstroke 200 represent the overlapping start and end points of thesegments. These overlapping areas are darker because they are each drawntwice—once when a segment ending with a particular point is drawn, andagain when the next segment beginning with the same point isdrawn—thereby reducing the transparency at the overlap. The result is anunintentionally non-uniform ink stroke. This is analogous to repeatedlymaking a glass window thicker, thereby making objects on the other sideof the glass more difficult to see by making the window darker. Thevariable transparency of the rendered ink is unexpected to the user whowould expect transparent ink to be rendered as transparent physical inkas applied to paper and/or over other ink.

There is also a need for providing various artistic features notprovided by current systems, such as dynamically rendering inkresponsive to variable width, pressure, speed, and angle of the pen.

SUMMARY OF THE INVENTION

Apparatus and methods are disclosed for dynamically renderingtransparent ink strokes that solves at least one of the problemsassociated with rendering transparent ink. Using the present invention,the rendering of electronic ink (or ink as used herein) is improved. Forexample, the ink stroke may be dynamically rendered as a stroke havinguniform transparency while it is being drawn. This may be performedwithout having to clear and redraw the entire screen.

To dynamically draw a transparent ink stroke, a computer system may drawonly the segment that has most recently been added to the stroke. Thesystem may further exclude areas of the new segment that overlap olderportions of the stroke from being painted more than once, which wouldotherwise make the older segments less transparent. For instance, thecolor settings of pixels in the overlapping areas may be frozen beforepainting the new segment. Freezing the color settings may reduce orprevent unintended non-uniformities in the ink stroke.

These and other features of the invention will be apparent uponconsideration of the following detailed description of preferredembodiments. It will be apparent to those skilled in the relevanttechnology, in light of the present specification, that alternatecombinations of aspects of the invention, either alone or in combinationwith one or more elements or steps defined herein, may be used asmodifications or alterations of the invention or as part of theinvention. It is intended that the written description of the inventioncontained herein covers all such modifications and alterations.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing summary of the invention, as well as the followingdetailed description of preferred embodiments, is better understood whenread in conjunction with the accompanying drawings, which are includedby way of example, and not by way of limitation with regard to theclaimed invention. In the accompanying drawings, elements are labeledwith reference numbers, wherein the first digit of a three-digitreference number, and the first two digits of a four-digit referencenumber, indicates the drawing number in which the element is firstillustrated. The same reference number in different drawings refers tothe same or a similar element.

FIG. 1 is an exemplary embodiment of both transparent andnon-transparent digital ink as they may be displayed, according to atleast one aspect of the present invention.

FIG. 2 is an exemplary embodiment of transparent digital ink as it maybe displayed, showing non-uniformities due to blending of multiplesegments.

FIG. 3 is an exemplary embodiment of transparent digital ink as it maybe displayed, without the non-uniformities of the ink shown in FIG. 2,and according to at least one aspect of the present invention.

FIG. 4 is a functional block diagram of an exemplary embodiment of acomputer system according to at least one aspect of the presentinvention.

FIG. 5 is a functional block diagram of an exemplary embodiment of anink rendering system according to at least one aspect of the presentinvention.

FIG. 6 is an exemplary flowchart showing steps that may be performed inorder to render transparent ink according to at least one aspect of thepresent invention.

FIG. 7 is an exemplary geometrical representation of stroke segmentsincluding circular pen tip instances and connecting quadranglesaccording to at least one aspect of the present invention.

FIG. 8 is an exemplary embodiment of digital ink corresponding to thestroke segments of FIG. 7 as it may be displayed, according to at leastone aspect of the present invention.

FIG. 9 is an exemplary geometrical representation of a frozen regionwithin a series of stroke segments, according to at least one aspect ofthe present invention.

FIG. 10 is a functional block diagram of an exemplary embodiment ofanother ink rendering system according to at least one aspect of thepresent invention.

FIG. 11 is an exemplary geometrical representation of a stroke includingdifferently-sized circular pen tip instances and connecting quadranglesaccording to at least one aspect of the present invention.

FIG. 12 is an exemplary embodiment of digital ink corresponding to thestroke of FIG. 11 as it may be displayed, according to at least oneaspect of the present invention.

FIG. 13 is an exemplary geometrical representation of a stroke includingdifferently-sized and differently-angled oval pen tip instances and aconnecting quadrangle according to at least one aspect of the presentinvention.

FIG. 14 is an exemplary embodiment of digital ink corresponding to thestroke of FIG. 13 as it may be displayed, according to at least oneaspect of the present invention.

FIG. 15 is an exemplary geometrical representation of a stroke includingdifferently-sized and differently-angled rectangular pen tip instancesand a connecting quadrangle according to at least one aspect of thepresent invention.

FIG. 16 is an exemplary embodiment of digital ink corresponding to thestroke of FIG. 15 as it may be displayed, according to at least oneaspect of the present invention.

FIGS. 17A and 17B are exemplary geometrical representations of a strokeincluding differently-sized and differently-angled rectangular pen tipinstances and two different possible connecting quadrangles according toat least one aspect of the present invention.

FIG. 17C is an exemplary representation of the stroke of FIGS. 17A and17B including all of the possible corner-connecting quadranglesaccording to at least one aspect of the present invention.

FIG. 18 is an exemplary embodiment of digital ink corresponding to thestroke of FIG. 17C as it may be displayed, including all possibleconnecting quadrangles, according to at least one aspect of the presentinvention.

FIG. 19 is a functional block diagram of an exemplary embodiment of yetanother ink rendering system according to at least one aspect of thepresent invention.

FIG. 20 is a geometric representation of an exemplary ink strokeillustrating the sample points therein as well as a fitting curve forposition, width, and rotation, in accordance with at least one aspect ofthe present invention.

FIG. 21 is a representation of a rendered exemplary ink stroke accordingto at least one aspect of the present invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Improved transparent ink rendering systems and methods are disclosed.The various embodiments of the invention are described in the followingsections: General Purpose Computing Environment, Ink Rendering System,and Ink Smoothing.

General Purpose Computing Environment

FIG. 4 illustrates a schematic diagram of an exemplary general-purposedigital computing environment that may be used to implement variousaspects of the present invention. In FIG. 4, a computer 400 such as apersonal computer includes a processing unit 410, a system memory 420,and/or a system bus 430 that couples various system components includingthe system memory to processing unit 410. System bus 430 may be any ofseveral types of bus structures including a memory bus or memorycontroller, a peripheral bus, and a local bus using any of a variety ofbus architectures. System memory 420 includes read only memory (ROM) 440and random access memory (RAM) 450.

A basic input/output system 460 (BIOS), containing the basic routinesthat help to transfer information between elements within computer 400,such as during start-up, is stored in ROM 140. The computer 400 alsoincludes a hard disk drive 470 for reading from and writing to a harddisk (not shown), a magnetic disk drive 480 for reading from or writingto a removable magnetic disk 490, and an optical disk drive 491 forreading from or writing to a removable optical disk 492 such as a CD ROMor other optical media. Hard disk drive 470, magnetic disk drive 480,and optical disk drive 491 are connected to the system bus 430 by a harddisk drive interface 492, a magnetic disk drive interface 493, and anoptical disk drive interface 494, respectively. The drives and theirassociated computer-readable media provide nonvolatile storage ofcomputer readable instructions, data structures, program modules andother data for personal computer 400. It will be appreciated by thoseskilled in the art that other types of computer readable media that canstore data that is accessible by a computer, such as magnetic cassettes,flash memory cards, digital video disks, Bernoulli cartridges, randomaccess memories (RAMs), read only memories (ROMs), and the like, mayalso be used in the example operating environment.

A number of program modules can be stored on hard disk drive 470,magnetic disk 490, optical disk 492, ROM 440, and/or RAM 450, includingan operating system 495, one or more application programs 496, otherprogram modules 497, and program data 498. A user can enter commands andinformation into computer 400 through input devices such as a keyboard401 and pointing device 402. Other input devices (not shown) may includea microphone, joystick, game pad, satellite dish, scanner or the like.These and other input devices are often connected to processing unit 410through a serial port interface 406 that is coupled to the system bus,but may be connected by other interfaces, such as a parallel port, gameport or a universal serial bus (USB). Further still, these devices maybe coupled directly to system bus 430 via an appropriate interface (notshown). A monitor 407 or other type of display device is also connectedto system bus 430 via an interface, such as a video adapter 408. Inaddition to the monitor, personal computers typically include otherperipheral output devices (not shown), such as speakers and printers. Inone embodiment, a pen digitizer 465 and accompanying pen or stylus 466are provided in order to digitally capture freehand input. Although adirect connection between pen digitizer 465 and processing unit 410 isshown, in practice, pen digitizer 465 may be coupled to processing unit410 via a serial port, parallel port, and/or other interface and systembus 430 as known in the art. Furthermore, although digitizer 465 isshown apart from monitor 407, in some embodiments the usable input areaof digitizer 465 be co-extensive with the display area of monitor 407.Further still, digitizer 465 may be integrated in monitor 407, or mayexist as a separate device overlaying or otherwise appended to monitor407.

The computer 400 can operate in a networked environment using logicalconnections to one or more remote computers, such as a remote computer409. Remote computer 409 can be a server, a router, a network PC, a peerdevice or other common network node, and typically includes many or allof the elements described above relative to computer 400, although onlya memory storage device 411 has been illustrated in FIG. 4. The logicalconnections depicted in FIG. 4 include a local area network (LAN) 412and a wide area network (WAN) 413. Such networking environments arecommonplace in offices, enterprise-wide computer networks, intranets andthe Internet.

When used in a LAN networking environment, the computer 400 is connectedto local network 412 through a network interface or adapter 414. Whenused in a WAN networking environment, the computer 400 typicallyincludes a modem 415 or other device for establishing a communicationsover wide area network 413, such as the Internet. Modem 415, which maybe internal or external, is connected to system bus 430 via the serialport interface 406. In a networked environment, program modules depictedrelative to the computer 400, or portions thereof, may be stored in aremote memory storage device.

It will be appreciated that the network connections shown are exemplaryand other techniques for establishing a communications link between thecomputers can be used. The existence of any of various well-knownprotocols such as TCP/IP, Ethernet, FTP, HTTP and the like is presumed,and the system can be operated in a client-server configuration topermit a user to retrieve web pages from a web-based server. Any ofvarious conventional web browsers can be used to display and manipulatedata on web pages.

Ink Rendering System

An exemplary ink rendering system 500 is illustrated in FIG. 5. Some orall of the ink rendering system 500 may be software, hardware, and/orfirmware, and may be a part of the computer system 400 or a separateunit. For instance, some or all of the ink rendering system 500 may beembodied as computer code stored in the RAM 450 as part of the operatingsystem 495, an application program 496, and/or another program module497. The ink rendering system 500 may include an ink storage 501 coupledto a rendering environment 502, which in turn may be coupled to agraphics toolbox 503, which in turn may be coupled to an output device504 such as a display screen (e.g., monitor 407) and/or printer. The inkstorage 501 may include information relating to ink including a filestructure having data points representing points of the ink. The filestructure may also include alternatively (or in addition to the datapoints) other ways to represent the ink including vectors betweenpoints, data points, stroke width information, and/or any other inkstorage scheme.

Stored ink may be rendered by calling the graphics toolbox 503 toperform various functions. The ink storage 501 may maintain a list ofrendering environments, one for each view in which the applicationrenders dynamically. Each rendering environment may maintain a list ofthe states, one for each stroke that is currently being dynamicallyrendered. Each state may represent the last pen tip position (e.g.,point) recorded and/or a queue of geometric regions that are furtherdescribed below. In at least one embodiment, the graphics toolbox 503has transparent painting capabilities, such as does Microsoft WINDOWSGDI+.

FIG. 6 illustrates an example of the operation of the ink renderingsystem 500. When a user draws a stroke, the ink rendering system 500 mayreceive a new pen tip position (step 601). More particularly, the inkstorage 501 may receive the new pen tip position. Pen tip positions maybe sampled and determined according to the position of the stylus 466upon the digitizer 465. Pen tip positions may further be determinedaccording to the position of the stylus 466 within a known input windowor area that defines a portion of the digitizer 466 surface. Forinstance, where the digitizer 465 and the monitor 407 are combined orco-extensive, there may be a predefined window displayed on thedigitizer 465 within which input from the stylus 466 may be accepted,e.g., for drawing an object and/or for entering text.

Pen tip positions may be sampled at a particular rate. The sampling ratemay be set at a rate at least high enough to capture sufficient pen tippositions based on the anticipated speed of a normal user. Once the newpen tip position is captured and received, the ink rendering system 500(e.g., in particular, the ink storage 501) may determine the area(and/or the contour that outlines and defines the area) that isassociated with the pen tip at the new position based on the size and/orshape of the virtual pen tip. This area is also known as a “pen tipinstance.” For example, where the virtual pen tip is considered to be a3-millimeter diameter circle, then the pen tip instance may be the3-millimeter diameter circle centered at the new pen tip position. Or,where the virtual pen tip is considered to be a rectangle of 2millimeters by 4 millimeters, then the pen tip instance may be the 2 by4 millimeter rectangle centered at the new pen tip position. Examples ofcircular pen tip instances 701, 702, 703, 704 are shown in FIG. 7. Thesize and shape of the pen tip instance are considered properties of thepen tip position. Where the entire stroke has the same size and/orshape, then the size and/or shape may be a property of the entire strokeas opposed to each pen tip position. Of course, any shape may be usedfor a pen tip. Circular pen tip instances are used here for simplicity.

Each time a pen tip instance is determined, that pen tip instance(and/or the associated pen tip position) may be stored for laterretrieval. Pen tip instances and/or positions may be stored as data in,e.g., RAM 450. Data representing the position (e.g., (x, y) coordinateposition), shape, and/or rotation of the pen tip instance may further bestored. Previous pen tip instances and/or positions may further bestored as part of digital ink storage such as in the serialized formatdescribed in U.S. patent application Ser. No. 09/852,799, entitled“Serial Storage of Ink and its Properties,” filed May 11, 2001.

Referring still to FIG. 6, the ink rendering system 500 may render anink segment that connects between the previous pen tip instance and anew pen tip instance in an ink stroke. To do so, the ink renderingsystem 500 may compute the new pen tip instance and/or one or moreconnecting quadrangles that connect between the new pen tip instance anda previous pen tip instance (step 602). Both the pen tip instances andthe connecting quadrangles are referred to herein as “regions.”

The new pen tip instance is associated with the new pen tip position,and may be centered about the new pen tip position. The new connectingquadrangle may be determined in a variety of ways, and the method fordetermining the connecting quadrangle may depend upon the shapes of thenew and previous pen tip instances. Various methods for determiningconnecting quadrangles will be discussed herein. Examples of connectingquadrangles 705, 706, 707 are shown in FIG. 7. A new region may bedefined as the new pen tip instance, the new connecting quadrangle, orthe combination (e.g., union) of the new pen tip instance and the newconnecting quadrangle. For example, the new region may be pen tipinstance 704, connecting quadrangle 707, or the union of pen tipinstance 704 and connecting quadrangle 707. Conventional graphicstoolboxes are capable of performing such a combination/union whenprovided with the shapes to be combined. In alternative embodiments,more than one new pen tip instance and/or new connecting quadrangle maybe the new region. For instance, two consecutive new pen tip instancesand their two corresponding new connecting quadrangles may be allunioned together as the new region. In this way, the method of FIG. 6does not necessarily need to be performed between each and every pen tipinstance.

The combination (e.g., union) of some or all of a plurality of previousregions may also be determined (step 603). These previous regions may bestored in a queue. A queue is an ordered list of items and is of afixed, dynamic, maximum, or other controlled length. For example, aqueue may have a maximum enforced length of 2, 3, or 4 items, althoughany length may be used. The queue may be configured as afirst-in-first-out (FIFO) type queue, as in a pipeline. Where themaximum length of the FIFO queue is surpassed by adding another item tothe queue, the oldest item is pushed out of the queue. The queue mayseparately store the actual items, or may have pointers that point tothe items stored elsewhere. Where the items are stored elsewhere, theymay be stored in a serialized or other format. In alternativeembodiments, the items in the queue may be any items of data thatrepresent some or all of the characteristics of pen tip positions and/orconnecting quadrangles. In still further embodiments, each item in thequeue may be a combined pen tip position and connecting quadrangle.

For example, referring to FIG. 9, where the new pen tip instance is pentip instance 905, the new connecting quadrangle is connecting quadrangle909, and the queue has a maximum length of 4 regions, the queued regionsto be combined may be pen tip instances 903, 904 (two regions) andconnecting quadrangles 907, 908 (two more regions, for a total of fourregions). The union of these queued regions is shown as the shaded areain FIG. 9. The arrow 910 indicates the direction of movement of the pentip, such that the pen tip instance 905 is the most recent and the pentip instance 901 is the earliest in time. Note that although connectingquadrangle 906 and pen tip instance 901 may have been in the queue at anearlier time, these two regions were later pushed out of the queue dueto the enforcement of its maximum length.

The ink rendering system 500 (in particular, e.g., the renderingenvironment 502) may freeze the color settings of the pixels (step 604)within the region defined by the combination (e.g., union) of the queuedregions (e.g., the shaded area in FIG. 9). The combined queued regionsthus become an excluding clip region that may be sent to the graphicstoolbox 503. Freezing the color settings means preventing the color andintensity of the pixels from changing. Thus, any further attempts atpainting the frozen pixels will have no effect on the color andintensity of the frozen pixels. This is important where the colors aretransparent, since the new connecting quadrangle (e.g., quadrangle 909)is likely to overlap with the union of the queued regions (e.g., theshaded area in FIG. 9). Without freezing the pixels in the queuedregions, the overlapping portion will undergo a change in transparencywhen the new regions are painted. Conventional graphics toolboxes arecapable of freezing the color settings of a group of pixels. Analternative to determining the union of the queued regions and thenfreezing the determined union region is to simply freeze each of thequeued regions individually. This alternative provides the benefit ofavoiding the step of determining the union. However, it increases thenumber of regions that need to be sent to the graphics toolbox forfreezing.

The new region may be sent to the graphics toolbox 503 for painting(step 605). The new region may be painted in a transparent ornontransparent color as desired. After the new regions are painted, someor all of the pixels in the excluding clip region may be unfrozen (step606). This step allows the color settings of the formerly frozen pixelsto again be modified. More generally, the ink rendering system 500 maydetermine whether pixels within the new pen tip instance and/or newconnecting quadrangle are also within the previous regions (such asthose regions in the queue). For those pixels that are, the colorsettings of those pixels may not be changed. For those pixels that arein the new pen tip instance but not within any of the previous queuedregions, the color settings may be changed.

The new region (e.g., connecting quadrangle 909) may then be pushed intothe queue (step 607). Where the queue has rules that determine the queuelength, one or more of the oldest regions may be pushed out of the queueas appropriate according to the queue rules. For example, referring toFIG. 9, a queue having a maximum of 4 regions may currently contain thefollowing regions in the following order: 907, 903, 908, and 904(wherein 904 is the oldest). When connecting quadrangle 909 (in thisexample, the new region) is pushed into the queue, then region 907 ispushed out the queue in order to maintain no more than 4 regions withinthe queue. Thus, the new queue would contain regions 903, 908, 904, and909 (in that order, with 903 being the oldest and 909 being the newest).The queue may have any maximum length, such as 1 region, between 2 and 4regions inclusive, between 5 and 10 regions inclusive, or between 10 and20 regions inclusive, 10 and 100 regions inclusive, or more. If thequeue length is too short, then it is likely that a new pen tip instancefrom a slow-moving pen may overlap a region recently dropped from thequeue, resulting in an unintended decrease in transparency in theoverlapping area. This results in an unexpected rendering of ink.However, as processing time increases with queue length, using a longqueue length may require the system to group numerous regions, objects,or shapes, thereby slowing the system during the rendering processand/or requiring higher processor speed to maintain adequaterepresentation of ink in real-time.

Further, a queue length that is allowed to be too long may preventcertain desirable overlapping of transparent ink, such as when writingthe script letter “e” as in FIG. 21. For example, if the queue lengthwere long enough to include all of points A through P of FIG. 21, thenthe overlapping as shown would not occur since all of the pixels in theshown segments would be part of the excluding clip region. But if themaximum queue length were set to, e.g., 4 regions, then at point M, asthe overlap begins to occur, the queue would contain only the regions ofthe connecting region between L and M, the region defined by the pen tipinstance at point L, the connecting region between K and L, and the pentip instance at point K. In such a case, the portion of the ink to beoverlapped would not be part of the excluding clip region. It is thusdesirable to use a queue length that balances the above considerations.For example, a queue with a length of 4 regions is a reasonablecompromise between quality and speed for a digitizer having a resolutionof about 12,000 by 9,000 pixels with a sampling rate of about 130samples per second. The maximal queue length may depend upon theresolution of the input digitizer, the display resolution, the samplingrate, the pen speed, user settings, application settings, and/or otherconsiderations. For instance, a larger maximal queue length may bedesirable with a higher digitizer resolution and/or a higher samplingrate.

The exemplary method of FIG. 6 may be repeated for each new region.Following the example discussed above, after the new region 909 ispushed into the queue, the method of FIG. 6 may be practiced where thenew region is pen tip instance 905. Once pen tip instance 905 is paintedin step 605 and the excluding clip region is unfrozen in step 606, thenthe pen tip instance 905 may be pushed into the queue and pen tipinstance 903 may be pushed out of the queue. This results in the queuecontaining regions 908, 904, 909, and 905.

As an alternative to determining the union of the queued regions and/orfreezing the pixels in the union, the intersection (i.e., overlap)between the new region and one or more of the queued regions may bedetermined. Instead of freezing the entire union of the queued regions,it may be desirable to freeze only those pixels in the intersection. Forinstance, where connecting quadrangle 909 is the new region, theintersection between the new region and the union of regions 907, 903,908, and 904 may be determined (as an alternative to step 603), and onlythose pixels in the intersection would be frozen (as an alternative tostep 604).

It is understood that one or more of the steps illustrated in FIG. 6 maybe performed in a different order, combined with another step(s), and/ordivided into further sub-steps as appropriate. For example, step 603 maybe performed prior to step 602 or even prior to step 601. Also, whileembodiments of the present invention are described with the connectionsbetween pen tip instances being line segments, it is appreciated thatthe ink between the pen tip instances do not have to be actual linesegments or quadrilaterals. The ink may include groupings of triangles,be bowed in shape, or assume a variety of shapes. One example of usingcurved lines is the advantage of being able to provide a degree ofsmoothing to an ink stroke.

The generation of connecting quadrangles is now discussed. Referring toFIG. 7, a particular exemplary ink stroke may include four circular pentip instances 701, 702, 703, 704, and three connecting quadrangles 705,706, 707. Connecting quadrangle 707 (for example) has four corners A, B,C, D, and four sides. The notation for an edge will refer to the endpoints of the edge. Thus, for example, the edge between corners A and Bwill be referred to as edge (or line or chord) AB.

The calculations for determining a connecting quadrangle may varydepending upon the relative shapes and sizes of the pen tip instances.Where the pen tip instances are both perfectly circular and of the samesize, as in FIG. 7, the connecting quadrangle 707 that connects pen tipinstance 703 and 704 may be defined by lines AC, BD that are tangent tothe outer edges of both pen tip instances, closed by the chords AB, CDthat connect them. Note that in this example where the pen tip instancesare of the same size and are circular, the chords AB, CD each definesthe geometric diameter of its respective pen tip instance. Also notethat in this example, the connecting quadrangles are each rectangleswith orthogonal sides. However, as will be seen in further examples, theconnecting quadrangles are not necessarily rectangles. They may be anytype of quadrangle such as parallelograms and trapezoids.

Thus far the exemplary pen tip instances have all been identically sizedcircles. However, this is not always the case. Pen tip instances may beof any shape, such as circles, rectangles (including squares),triangles, ovals, blobs, stars, lines, arcs, points, or polygons. Pentip instances may be symmetric or asymmetric. An example of anasymmetric pen tip instance is one configured to emulate the tip of acalligraphy pen. Pen tip instances may also be of varying size, suchthat two consecutive pen tip instances in the same set of ink may be ofdifferent sizes. Pen tip instances may further be of varying shape, suchthat two consecutive pen tip instances in the same set of ink may be ofdifferent shapes. Pen tip instances may further be of varying rotation,such that two consecutive pen tip instances in the same set of ink maybe rotated at different angles. Of course, where the pen tip instance isan exact circle, the angle of rotation is meaningless. The rotation of apen tip instance is also considered a property of each pen tip positionand/or the entire stroke. To account for these potential variations inpen tip instance characteristics, another exemplary ink rendering system1000 is shown in FIG. 10. The ink rendering system 1000 includes, or iscoupled to, a pen device 1000 that feeds the (x, y) coordinates of thepen tip to a contour generator 1002. The pen device 1000 may also feedthe pen tip instance size and/or rotation (e.g., angle) for each pen tipinstance. The contour generator 1002 may be configured to generate acontour defining the outline of the pen tip instance based on theinformation provided by the pen device 1000, as well as informationabout the particular pen tip instance shape selected. Alternatively,there may be a plurality of contour generators 1002 each specializing ina different shape or family of shapes. For example, there may be a firstcontour generator that is configured to generate contours for circularpen tip instances and a second contour generator that is configured togenerate contours for rectangular (including square) pen tip instances.

The contour generator 1002 (or another specialized contour generator)may also generate contours that define the shape of the connectingquadrangles, based on the received and utilized pen tip instancecharacteristics and positions. The contour generator 1002 may then sendthe generated contours to a graphics toolbox 1004. Where the ink istransparent, the contour generator 1002 may communicated with thegraphics toolbox 1004 via a rendering environment 1003, and the methodof FIG. 6 may be implemented. The graphics toolbox 1004 may fill orfreeze the provided contours as appropriate and then output pixel valuesto an output device 1005 such as the monitor 407.

Referring to FIG. 11, an exemplary ink stroke has four pen tip instances1100, 1101, 1102, 1103 of different sizes. Since the pen tip instancesare circular, rotation is less important in this example and will beignored in the present example. As this ink stroke was drawn, the sizeof the pen tip instances changed from medium (pen tip instance 1100), tolarger (pen tip instances 1101, 1102), and then smaller (pen tipinstance 1103). The size, rotation, and/or pen tip shape may be adjustedautomatically by a software application running on the computer 400and/or by the user. For example, the user may have pressed thenstylus/pen 466 down against the digitizer 466 with additional pressure,or may have moved the stylus/pen 466 more slowly, to select larger pentip instances. Or the user may physically rotate the pen along itslongitudinal axis in order to obtain different rotated pen tipinstances. The connecting quadrangles for different-sized circular pentip instances are, in some embodiments, generated by determiningtangential lines (e.g., lines AC and BD in FIG. 11) between the pen tipinstances and then connecting those lines at the tangents withconnecting chords (e.g., chords AB, CD in FIG. 11).

Referring to FIG. 13, the same method may be used as in FIG. 11 fordetermining connecting quadrangles (or other shapes). An exemplary inkstroke may include oval pen tip instances 1301, 1302. The connectingquadrangle may, in one example, be determined by calculating the linesthat run tangent between the two ovals. In this case, those tangentiallines would be lines AC and BD in FIG. 13. The tangential lines wouldthen be closed by connecting their endpoints at the tangents with linesAB, CD. Note that although these ovals are of different rotationalangles, the rotation does not matter for ovals when determining theconnecting quadrangles.

Next in FIG. 15 is shown an exemplary embodiment of a connectingquadrangle between two rectangular pen tip instances 1501, 1502, eachhaving a different size and rotation. Although there are many possibleconnecting quadrangles, in this example, a connecting quadrangle 1503connects corners A and E, corners A and C, corners C and G, and cornersG and E. Another connecting quadrangle that could be used would connectcorners A and H, corners D and F, corners B and G, and corners C and H.Another example is shown in FIGS. 17A and 17B, showing two differentconnecting quadrangles 1703, 1704 that could be used to connect two pentip instances 1701, 1702. Connecting quadrangle 1703 connects corners Aand A′, corners C and C′, corners A and C, and corners A′ and C′.Connecting quadrangle 1704 connects corners B and B′, corners D and D′,corners B and D, and corners B′ and D′.

It may be desirable to utilize a connecting quadrangle that connectsbetween the outermost portions of the two pen tip instances to beconnected. For instance, where the two pen tip instances are bothpolygons (i.e., closed shapes having only straight edges connected atcorners), it may be desirable to connect the outermost corners togetherto provide for the largest area possible covered by the connectingquadrangle. Such an embodiment may in many cases provide a very smoothtransition between pen tip instances and a higher-quality ink that ispleasing to the eye. Also, some or all of the possible connectingquadrangles (or a subset thereof) may be determined, and the determinedquadrangles may be combined together (e.g., by taking their collectiveunion) into a single connecting region. For example, referring to FIG.17C, all of the possible connecting quadrangles that connect the cornersof the pen tip instances 1701, 1702 are shown. A result of this is thatevery corner of pen tip instance 1701 is connected to every corner ofpen tip instance 1702 via an edge of at least one of the connectingquadrangles. This method may be extended to any polygon having anynumber of sides and corners. FIG. 18 illustrates the resulting ink whenall of the connecting quadrangles of FIG. 17C are combined together.

FIGS. 8, 12, 14, 16, and 18 illustrate the rendered ink that correspondsto the pen tip instances and connecting quadrangles in FIGS. 7, 11, 13,15, and 17C respectively. The rendered ink in these figures is a resultof using the rendering system 1000 as described.

Ink Smoothing

The ink-rendering process may also include smoothing the ink. Smoothingmay be performed by the rendering system 500, 1000, such as by thegraphics toolbox 503, 1004, using known smoothing functions. Anotherexample of an ink rendering system 1900 is illustrated in FIG. 19. Theink rendering system 1900 includes a pen device 1901, a smoothingapplication or subroutine 1902, a curve-sampling application orsubroutine 1903, a contour generator application or subroutine 1904,and/or a recipient 1905, which may be a graphics toolbox. In operation,the pen device 1901 (e.g., a digitizer and pen) may measure the pen's(x, y) location on the digitizer. The pen device 1901 may furtherdetermine the intended rotation angle and/or size of the pen tip. Thesmoothing application 1902 may receive a plurality of sampled pen tippositions, pen tip instance sizes, and/or angles of pen tip instancerotation and may smooth the position, size, and/or rotation amongst theplurality of pen samples. The curve-sampling algorithm 1902 may samplethe smoothed (x, y) curve, the smoothed size function, and/or thesmoothed rotation function and may output samples of these smoothedfunctions to the contour generator 1904. The contour generator 1904 maythen generate the desired contours such as the pen tip instances and/orthe connecting quadrangles, and forward these contours on to therecipient 1905.

Smoothing may be performed on the size and/or rotation parameters. Therendering system 1900 may use any smoothing technique such as leastsquares fitting. To smooth ink, samples of the ink may need to be taken.These samples may be taken anywhere along the ink stroke, but at leastone sampling technique is to sample the locations that were originallysampled from the pen (i.e., the sampled pen tip locations).

An exemplary smoothing function may be implemented by the ink renderingsystem 1900 (more particularly, by, e.g., the smoothing application1902) as follows for each sample along the ink stroke:(smoothed width)_(i) =A ₁*(original width)_(i−1) +A ₂*(originalwidth)_(i) +A ₃*(original width)_(i+1),  (1)where A₁, A₂, and A₃ are constants that may be chosen as desired, i isthe sample number along the sampled ink stroke, “smoothed width” is thewidth of the ink stroke at sample i after smoothing, and “originalwidth” is the width of the ink stroke at sample i before smoothing. Insome examples, the sum of these three constants should equal unity. Acombination of A₁=0.25, A₂=0.5, and A₃=0.25 works well. Angle ofrotation can also be smoothed using any of the method for smoothingwidth, including substituting “smoothed width” and “original width” inequation 1 with “smoothed angle” and “original angle,” respectively. Inanother embodiment, both size and angle may be smoothed for the same inkstroke.

Referring to FIG. 20, an exemplary ink stroke is shown having sampledpoints C₁ through C_(n) (each denoted with an “x”). Each sampled point Calso has an associated size and/or rotation. Size, or width, at samplepoint C_(i) will be denoted as W_(i), and its associated rotation willbe denoted as R_(i). It may be desirable to smooth the sampled ink as tothe (x, y) positions of the sample points, the size or width of thesampled points, and/or the rotation of the sampled points.

For example, using a least-squares method for smoothing, the followingalgorithm may be used such that the fitting curve P minimizes thefollowing:minΣ{a(C_(i)−P_(i))²+b[W(C_(i))−W(P_(i))]²+c[R(C_(i))−R(P_(i))]²},  (2)where a, b, and c are optional weighting constants; P_(i) are thelocations of the points on the fitting curve P; W(P_(i)) are thesizes/widths for each point P_(i); and R(P_(i)) are rotations for eachpoint P_(i). The fitting curve P may be any curve desired, such as onechosen from the family of parametric or Bezier curves. In effect,width/size and/or rotation are treated as additional dimensions otherthan position. Any subcombination of the dimensions in fitting a curvemay also be used. For example, the third term c[R(C_(i))−R(P_(i))]² maybe dropped from equation 2 so that rotation is not considered. Or, thesecond term b[W(C_(i))−W(P_(i))]² may be dropped from equation 2 so thatwidth or size is not considered. Or, the first term a(C_(i)−P_(i))² maybe dropped from equation 2 so that sample position is not considered.Alternatively, both the first and second terms, or both the first andthird terms, may be dropped from equation 2 so that only rotation oronly width are considered in determining the fitting curve parameters.

While exemplary systems and methods embodying the present invention areshown by way of example, it will be understood, of course, that theinvention is not limited to these embodiments. Modifications may be madeby those skilled in the art, particularly in light of the foregoingteachings. For example, each of the elements of the aforementionedembodiments may be utilized alone or in combination with elements of theother embodiments. For example, while connecting quadrangles arediscussed herein as a particularly advantageous shape, any shape ofconnecting regions other than quadrangular-shaped regions may be used.Also, while the above description discussed pen tip positions as beingdefined by (x, y) in a rectilinear coordinate system on the digitizer,any other coordinate system, such as polar, may be used.

1. A method for dynamically rendering a digital ink stroke, comprisingthe steps of: receiving a new pen tip instance; determining a firstregion based on the new pen tip instance; determining a second regionbased on a previous pen tip instance; freezing a color of each of aplurality of pixels within an intersection of the first and secondregions; and painting the first region while the color of the pixelswithin the intersection is frozen, wherein said painting the firstregion comprises applying a new color setting to a plurality of pixelsthat are within a third region preceding the second region.
 2. Themethod of claim 1, wherein the second region is a combined set ofregions including at least one previous pen tip instance.
 3. The methodof claim 2, wherein the second region is a union of the set of regions.